Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter

• URL: http://arxiv.org/abs/2609.00159v1
• Date: Mon, 31 Aug 2026 18:00:17 GMT
• Title: Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter
• Abstract summary: We show that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter.<n>Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.

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